Magnetization dynamics for the layman: Experimental Jacques Miltat - - PowerPoint PPT Presentation

Magnetization dynamics for the layman: Experimental

Jacques Miltat Université Paris-Sud & CNRS, Orsay

École de Magnétisme Brasov, Rumania, September 2003

With the most generous help of Burkard Hillebrands (Symposium SY3, ICM-Rome, July 2003

Magnetization dynamics (classical description)

Landau-Lifshitz-Gilbert equation of magnetization motion

: gyromagnetic ratio : acting effective magnetic field (embedding the pulsed field) : Gilbert damping parameter

dM dt = −γ0 M× Heff

[ ]+ α

Ms M× dM dt       γ0

Heff

α α ≠ 0 α = 0 d dt M2 t

( )= 0

d dt M t

( )⋅ H

[ ]= 0

Magnetization dynamics (Cont'd)

Landau-Lifshitz equation with damping

1+α2

( )

dM dt = −γ0 M× Heff

[ ]−αγ0

M s M× M× Heff

[ ]

{ }

Bloch-Bloembergen Equation

dM x,y dt = −γ0 M× Heff

[ ]x,y − M x,y

T2 dMz dt = −γ0 M× Heff

[ ]

z − M z

T1 T1 T2

: Longitudinal relaxation time : Transverse relaxation time

Magnetization dynamics (Cont'd)

Spin waves formalism : kinetic equations (valid for exchange dominated spin waves)

M = Ms −γ0h n' Mz = M s −γ0h n0 + n'

( )

n0 n'

: Number of magnons with (infinite wavelength) : Number of all other magnons

k = 0

Consider the following rate equations as an example (˜ "TWO Magnons Model"):

dn0 dt = − λ0k + λ0σ

( )n0

dn' dt = λ0k n0 − λkσ n'

Where, is the probability of destruction of a magnon with the production of a magnon, and are the probability of disappearance of and magnons, respectively

k = 0 λ0k k ≠ 0 λ0σ λkσ k = 0 k ≠ 0

Magnetization dynamics (Cont'd)

Combining :

M = Ms −γ0h n' Mz = Ms −γ0h n0 + n'

( )

dn0 dt = − λ0k + λ0σ

( )n0

dn' dt = λ0k n0 − λkσ n'

One gets for the sole damping term :

and

dM dt = −λ0k M − Mz

( )+ λkσ Ms − M

( )

dMz dt = +λ0σ M − M z

( )+ λkσ Ms − M

( )

Magnetization dynamics (Cont'd)

I. Thus, depending on the formalism, one may define ONE, TWO or MORE parameters defining damping processes ..... II. This problem remains a yet unsolved issue of spin dynamics

Small Excitations

I. FMR in inhomogeneous films : a numerical experiment II. Local dynamics III. Spin waves quantization and localization IV. Magnetic noise spectra

FMR in inhomogeneous films

In the absence of inhomogeneities, the damping parameter is, within the LLG formalism, related to the derivative of the absorbed power through:

α = 3γ0∆H pp /2ωr

For weak inhomogeneities treated as perturbations, the two-magnon model has been considered valid [?], whereas for large inhomogeneities the linewidth may be considered as a superposition of linewidths from independently resonating regions. A ferrromagnetic resonance experiment measures both a resonance frequency and a line width. The latter reflects the effects of both damping AND inhomogeneity.

α ? (schematic)

• S. Ingvarsson et al. CondMat 0208207

See also: S. Mizukami et al. Jap. J. Appl. Phys. 40 (2001) 580

• α directly correlated to electron scattering

"Ordered" "Disordered"

Multimode damping in inhomogeneous films

R.D. McMichael, D.J. Twisselmann, A. Kunz, PRL 90, 227601 (2003) Dealing with inhomogeneities: Calculation of eigenmodes in films taking defects into account

Precession frequencies of 3001 spin waves with resonant frequencies closest to the uniform resonance mode

Multimode damping in inhomogeneous films

R.D. McMichael, D.J. Twisselmann, A. Kunz, PRL 90, 227601 (2003) I. FMR signals are simulated by replacing each eigenmode spike with a Lorentzian peak with FWHM given by the LLG linewidth for α=0.01. II. This process makes use of a single damping coefficient

Multimode damping in inhomogeneous films

R.D. McMichael, D.J. Twisselmann, A. Kunz, PRL 90, 227601 (2003) I. Results exhibit a clear transition from a "TWO-Magnon" type behaviour to a "LOCAL Resonance" mode II. No comparison to experimental results, yet

Local dynamics in square Py elements

Quantized magnetostatic modes under high frequency drive field Spatially resolved FMR-Kerr-Microscopy: Synchronization of laser pulses with microwave source

• S. Tamaru, J.A. Bain et al., J. Appl. Phys. 91, 8034 (2002)

theory: K. Guslienko, R. Chantrell, A.N. Slavin, PRB, in press

Response at the center of a 50*50 µm2 Py square, 100 nm thick @ 7.04 GHz Amplitude (top) and phase (bottom) response vs position for P1-P5 @ 7.04 GHz

Spin dynamics in closure domains

J.P. Park et al., Phys. Rev. B. 67, 020403(R) (2003) See also J. P. Park et al., PRL 89 (2002) 277201 (spin-wave modes in wires)

Polar Kerr response vs position and Fourier Transforms in 5 µm*5 µm Py platelets Average of the frequency power spectrum averaged over the whole sample Simulations: Top: Unconvolved Bottom : Convolved

Spatially resolved spin-wave modes in magnetic wires

J.P. Park et al., PRL 89, 277201 (2002)

Polar Kerr rotation vs position in 5 µm width, 18 nm thick Py wires (BWVMS geometry) Left: Time-domain images: 5 µm width Py wires Right: Frequency domain Note the absence of edge mode in the DE geometry Comparison between experiments and LLG simulations Note the tendency towards a uniform mode at low field

Localized thermal spin-waves in magnetic wires

• C. Bayer et al., Appl. Phys. Lett. 82,

607 (2003)

• 0,50
• 0,25

0,00 0,25 0,50 50 100 150 200 250 300

z

H Stripe 1 µm wide Frequency (arb. units) Internal field (Oe) z/w

BLS spectrum, q=0.47 105 cm, He=800 Oe PSSW: thickness mode

Quantized spin waves in wires: BLS studies

35 mm NiFe wires 1.75/0.3 µm

• 25
• 20
• 15
• 10
• 5

q-DE PSSW

2.11·10

5cm

• 1

2.00 1.87 1.72 1.57 1.40 1.22 1.03 0.83 0.63 0.42 0.21·10

5cm

• 1

q|| = 0

Intensity (arb. units) Frequency shift (GHz)

localized dispersionless modes

S.O. Demokritov, B. Hillebrands, in: „Spin dynamics in confined magnetic structures“, Topics in Applied Physics 83 (2003), Springer

0,0 0,5 1,0 1,5 2,0 2,5 6 8 10 12 14 16

film d = 40 nm Spin wave frequency (GHz) q|| (10

5 cm

• 1)

A common idea in all these studies : ?

A common idea in all these studies : The internal field is not homogeneous

Spin wave propagation

plane of light incidence magnetic field configuration Hstat H (t)

pulse

X Y Z

vgroup = 6.6 cm/µs

t [ns]

0.00 0.40 0.85 1.35 1.85 2.30

Tpulse 3 ns ≈ BiLuIG

3.75 4.20 2.80 3.25 4.70 5.15 5.65 6.10 6.60 7.05 7.55 8.00 8.50 9.00

3.2 mm 1.8 mm

Hpulse = 1 Oe, 3 ns Hstat = 40 Oe

FFT signal frequency [GHz] 0.0 0.2 0.1 0.3 0.4 0.5 0.6 0.7

• 0.1
• 0.2
• 0.3
• 0.4
• 0.5
• 0.6
• 0.7

X [mm] = ν0 = 0.83 GHz

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

νk = 1.05 GHz MO signal time [ns] 0.0 0.2 0.1 0.3 0.4 0.5 0.6 0.7

• 0.1
• 0.2
• 0.3
• 0.4
• 0.5
• 0.6
• 0.7
• 1

1 2 3 4 5 6 7 8 9

X [mm] =

a) b)

x: distance to stripeline, x=0 group velocity ν0: uniform mode νk: propagating spin wave

• J. Fassbender, in: „Spin dynamics in

confined magnetic structures II“, Topics in Applied Physics 87 (2003), Springer

Magnetic noise spectrum in GMR device

• N. Stutzke, S.L. Burkett, S.E. Russek,
• Appl. Phys. Lett. 82, 91 (2003);
• J. Vac. Soc. Tech. A 21, 1167 (2003)

NiFe/CoFe/Cu/CoFe/Ru/CoFe/IrMn- spin valve device 1* 3 µm2 Good fit by single-domain noise model with noise power proportional to ima- ginary part of dynamic susceptibility

Vn f

( )= I∆R

kBT 2π fµ0M s

2V

χt

" f

( )

Resonant behaviour of the noise voltage

Large excitations, Switching

I. Conventional switching II. Precessional switching III. rf assisted switching IV. wall motion in nano-wires

Early Experiments: Pulsed field along the easy axis

EXPERIMENTS SIMULATIONS

• B. C. Choi et al., J. Appl. Phys. 89 (2001) 7171

Switching mechanisms dominated by wall motion, domain expansion and nucleation, leading to an overall complexity

Time resolved Kerr microscopy: a different kind of excitation

• Y. Acremann et al., Science 290, 495 (2000)

6 µm Co disk, excited with current pulse in microfabricated loop, magneto-optic Kerr microscopy

Precessional switching

Simultaneously demonstrated at MMM Seattle in fall 2001 by:

• Nijmegen group: pulse shaping by two fs laser pulses
• Th. Gerrits et al., Nature 418, 509 (2002)
• NIST Boulder group: MR measurement
• S. Kaka and S.E. Russek, Appl. Phys. Lett. 80, 2958 (2002)
• Orsay group: MR measurement, multiple switching

H.W. Schumacher et al., Phys. Rev. Lett. 90, 017201 (2003)

• 1.0
• 0.5

0.0 0.5 1.0

• 1.0
• 0.5

0.0 0.5 1.0

• 0.1

0.0 0.1 0.2

Mz M

x

My

Precessional switching : principle

A two-step process particularly well suited to thin films:

1) The initial torque moves the magnetization out of plane 2) The torque due to the demagnetizing field allows for magnetization rotation along a trajectory that remains close to the plane of the film

Experimental Method B M

Pulse line detection line

magneto resistive device: TMR, GMR

I V(M,t)

pulse generator (100 ps – 10 ns) sampling

• scilloscope

current source (50 Ω)

MR response s a m p l i n g

• s

c i l l

• s

c

• p

e ( 5 G H z )

H.W. Schumacher et al., APL 2002

Hard axis pulse response: large angle precession

• Pulse field above

anisotropy field HA

• Tpulse = 2.5 ns ps,

HPulse = 150 Oe

• pinned layer aligned

along easy axis

• static field: offset compensated
• large angle precession

about HPulse (>90°)

• good LLG fit with

α = 0.02-0.03 Long hard axis pulse: Magnetization response Calculated pinned layer response

TMR sample, 1.1x3.8 µm2

Hard axis pulse response: TMR elements

Magnetization response

TMR sample, 1.1x3.8 µm2

Short hard axis pulse:

An even better agreement with a simple single spin model: α = 0.02

Tunneling Magneto-Resistance (TMR) Samples

free ferromagnetic layer Tunneling

• xide

pinned FM layer antiferromagnet

Sample dimensions: Cells: 1x2 µm2-2x4 µm2 PL: 0.25x5 µm2 AlOx: 0.25 µm HC ~ 5 - 30 Oe HBias ~ 0 - 20 Oe R ~ 1-3 kΩ MR ~ 20 %

10 20 30 40 1000 1050 1100 1150 1200 1250

TJS1607B Structure a4 I = 100 µA ∆R = 200 Ω ∆R/R = 20 %

Junction Resistance (Ω) External Field (Oe)

Pulse line on top: Glass PL SL SL AlOx AlOx

1x4 µm2

Ta 30 Å NiFe 30 Å CoFe 20 Å Al 11A ox. CoFe 25 Å MnCrPt 300 Å NiFe 70 Å Ta 90 Å

H.W. Schumacher et al., JAP 2003 Exchange_Bias Field

Experiment (CNRS Orsay):

Precessional switching H

Bit “0” Bit “1” Switching by pulsed magnetic field perpendicular to direction of magnetization

H.W. Schumacher et al., Phys.

• Rev. Lett. 90, 017204 (2003)

δt20-80%~130ps

Quasi-Ballistic Switching

H.W. Schumacher et al., APL 2002

δt20-80%~130ps

GMR, 2.3 x 5 µm2 Vpulse = 10 V Hpulse = 236 Oe H.W. Schumacher et al., Phys.

• Rev. Lett. 90, 017204 (2003)

Phase Coherence (GMR Samples)

GMR, 2.3 x 5 µm Vpulse = 10 V Hpulse = 236 Oe colour encoded time resolved GMR signal Coherent reversal: Tpulse ≈ (n+1/2) Tprec

1 2

Time (ns) Pulse Duration (ns)

0.2 0.4 0.6 0.8 1.0

n = 1 n = 2 n = 3 switch switch switch Precession

• n pulse

pulse application time n = 4 switch No switch Initial state Decay Rise H.W. Schumacher et al., Phys. Rev. Lett. 90, 017204 (2003)

Multiple switching

H.W. Schumacher et al., Phys.

• Rev. Lett. 90, 017201 (2003)

200 400 600 800 12 8 4

Pulse length (ps) Pulse att. (dB)

12 8 4 200 400 600 800 200 50 50 200

(b) (a)

Pulse att. (dB)

100

Field (Oe)

100

Field (Oe)

Precessional switching by optical pulse shaping

• Th. Gerrits et al., Nature 418, 509 (2002)

Precessional switching

• S. Kaka and S.E. Russek, Appl. Phys. Lett. 80,

2958 (2002) single domain simulation 0.45* 1.15 µm2 spin valve magnetoresistance measurement

New techniques for excitation and switching

• generation of fast current pulses by Shottky barriers
• Y. Acremann et al., Nature 414, 52 (2001)
• rf field assisted switching
• C. Thirion, W. Wernsdorfer, D. Mailly, Nature, in press
• microwave excitation and synchronization of laser pulses

with microwave source

• S. Tamaru, J.A. Bain et al., J. Appl. Phys. 91, 8034 (2002)

Ultrafast magnetic fields by a Schottky diode

• Y. Acremann et al., Nature 414, 52 (2001)

New switching techniques: rf field assist. switching

• C. Thirion, W. Wernsdorfer, D. Mailly, Nature Materials 08/2003

modified Stoner astroid non- switching switching switching

Faster magnetic walls due to roughness in wires

Counter-intuitive behaviour: DW speed increases with increasing roughness Roughness

• inhibits Walker velocity break-

down found in sample without imperfections

• creates domain wall coercivity

defect-free with defects (dm/dt)2:

• Y. Nakatani, A. Thiaville, J. Miltat, Nature Materials, (August 2003)

Experiment: D. Atkinson et al., Nature Materials 2, 85 (2003)

A hint towards more complexity: Spin pumping

• FMR linewidth of thin layer (F1)

increases in presense of thick layer (F2)

• spin current from precessing layer to

non-precessing, off-resonant layer: additional Gilbert damping

• interface damping depends on

precession angle

• spin pumping is directly related to the

dynamic response of the interlayer exchange coupling

• B. Heinrich, in: „Ultrathin magnetic structures III“,
• B. Heinrich, J.A.C. Bland (eds), Springer;
• Phys. Rev. Lett. 90, 187601 (2003)

GaAs(001) / 16Fe / 14Au / 40Fe / 20Au

Ultra-fast phenomena : thermalization of spin populations in ferromagnetic films

• L. Guidoni et al., PRL 89 (2003) 017401

Experimental set-up

ε = ˜ ε

xx

1 i ˜ Q 0 −i ˜ Q 1 1           ; ˜ ε

xx =ε'xx +iε''xx

˜ Q = q'+iq''

Temporal evolution of the optical parameters: note that ∆q/q follows the same dynamics as the Faraday rotation, the ellipticity, the real and imaginary parts of ε for t> 150 fs

The ultrafast spin dynamics occurs during the thermalization of the electronic populations with a characteristic time

• f about 50 fs

Ultra-fast phenomena : Generation of coherent spin-waves

M van Kampen et al., PRL 88 (2002) 227201

Experimental set-up

Precession at "long" times arises from the

• ut of equilibrium

magnetization

• rientation post

thermalization

Existence of two time scales

Take away message

I. Observations all linked to the inhomogeneous character of the (internal) effective field II. Defining the true magnetic dynamical properties of a thin film in its environment remains a challenging issue III. Extremely fast development of experimental techniques (all optical, XMCD/XMLD microscopy, PEEM …) IV. Yet, the 10 ps, 1 nm resolutions ultimate goal seems far away V. Failing to have such tools, it will remain extremely hazardous either to stick to the LLG formalism or discard it on various grounds VI. Temperature effects have almost not yet been addressed in the spin dynamics of confined structures